Animesh Biswas

Archie J. Huang, Animesh Biswas, Shaurya Agarwal

This research contributes to the advancement of traffic state estimation methods by leveraging the benefits of the nonlocal LWR model within a physics-informed deep learning framework. The classical LWR model, while useful, falls short of accurately representing real-world traffic flows. The nonlocal LWR model addresses this limitation by considering the speed as a weighted mean of the downstream traffic density. In this paper, we propose a novel PIDL framework that incorporates the nonlocal LWR model. We introduce both fixed-length and variable-length kernels and develop the required mathematics. The proposed PIDL framework undergoes a comprehensive evaluation, including various convolutional kernels and look-ahead windows, using data from the NGSIM and CitySim datasets. The results demonstrate improvements over the baseline PIDL approach using the local LWR model. The findings highlight the potential of the proposed approach to enhance the accuracy and reliability of traffic state estimation, enabling more effective traffic management strategies.

Animesh Biswas, Archie Huang, Shaurya Agarwal et al.

This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and temporal nonlocal interactions, allowing the velocity at a given point to depend on aggregated downstream traffic conditions over a finite time horizon. This structure provides a more realistic representation of driver anticipation and reaction behavior. In addition to developing the model, we establish several key analytical properties that clarify the theoretical foundations of the proposed nonlocal framework. To assess its practical relevance, we conduct a detailed empirical validation using high-resolution NGSIM trajectory data. The results demonstrate that the spatial-temporal nonlocal model significantly improves the reconstruction of traffic density fields compared with traditional local macroscopic models, particularly in regimes where anticipation effects dominate. These findings highlight the potential of spatial-temporal nonlocal traffic dynamics as a robust theoretical and data-driven framework for capturing complex traffic behavior.